Calculating the vacancy formation energy in metals: Pt, Pd, and Mo

The predictive power of first-principles calculations of vacancy formation energies in metals (Pt, Pd, Mo) is improved by adding a correction for the intrinsic surface error in current implementations of density functional theory. The derived correction is given as a function of electron density; it can be explicitly applied to a wide range of systems. Density functional theory, contrary to claims in previous work, underestimates the vacancy formation energy when structural relaxation is included. This is the case whether using the local density- or the generalized gradient approximation for the exchange-correlation energy. With corrections for the intrinsic surface error we reach excellent agreement between calculated values using the two exchange-correlation functionals. Our final values for the three vacancy formation energies are 1.16, 1.70, and 2.98 eV for Pt, Pd, and Mo, respectively. The numbers are in good agreement with experimental data. We also calculate the barrier for vacancy diffusion in Pt to 1.43 eV.